Numerous sensor devices are already known which are used for controlling lighting devices of motor vehicles. Such a sensor device is described, for example, in the German Published Patent Application No. 199 33 642. It has a bulky light-guiding member made of transparent plastic that is secured on the window of a motor vehicle via a coupling medium. This light-guiding member images the radiation of light from various solid-angle regions onto receivers, which, for their part, control the lighting devices via a suitable control device. Since the lighting conditions in the forward direction of the vehicle are particularly relevant for controlling the lighting devices, the light-guiding member must be arranged on the windshield of the motor vehicle, which restricts the visual range of the driver because of the expansion of the sensor device.